I have a boardgame call Enemy Coast Ahead: The Dambusters in which enemy FLaK poses a major problem.
Under some circumstances the game "AI" throws three instead of two dice and if the sum of any two of them is within a certain interval a hit is scored. Furthermore if doubles are rolled and that gives a hit the doubles are re-rolled. If that is a hit but not a re-roll the hit is score and then it stops. If that is a hit and a double hit is score and another re-roll follows.
For starters I'd just like to know the probability of the sum of the two dice being 2,3 or 4 when rolling three dice.
As I see it(and I have not idea whether I right): Dice 1,2 and 3, denoted A, B and C can roll a lethal combbination as AB, BC or AC.
At Flak Level 1 the lethal range is 2-4. That gives 1/36 + 2/36 + 3/36=6/36 =1/6 for a Hit.
Using three dice and combinations AB, DC and AC just one of them is enough for a hit so since OR goes into it we get 1/6 for each 1/6 + 1/6 + 1/6 = 1/2.
Best Regards Peter